Convergence of the the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography

Abstract : We prove the convergence of the hydrostatic reconstruction scheme with kinetic numerical flux for the Saint Venant system with Lipschitz continuous topography. We use a recently derived fully discrete sharp entropy inequality with dissipation, that enables us to establish an estimate in the inverse of the square root of the space increment ∆x of the L 2 norm of the gradient of approximate solutions. By Diperna's method we conclude the strong convergence towards bounded weak entropy solutions.
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Submitted on : Friday, September 6, 2019 - 9:52:43 AM
Last modification on : Saturday, September 7, 2019 - 1:11:06 AM

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François Bouchut, Xavier Lhébrard. Convergence of the the kinetic hydrostatic reconstruction scheme for the Saint Venant system with topography. 2019. ⟨hal-01515256v2⟩

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